I think the more important point to be made isn't that there is a lot of variation in when hakama go on (styles do vary), but about how you present yourself at a dojo outside your system.

...I'll suit up however *they* feel is appropriate for their dojo. I ain't there to teach -- I'm there as a student.

The bigger question is about proper manners before you ever step onto someone else's mat to train.

...I *always* sit in the super newbie position if I'm visiting a dojo because I *am* the super newbie there. They may ask me to move according to my rank within my own style, but that's up to them to decide.